Eliminating spin-asymmetric orbital instabilities of unrestricted MRSF-TDDFT via selective Jacobi rotation

Abstract

Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory (MRSF-TDDFT) has emerged as a promising linear-response framework capable of addressing multireference electronic structure, conical intersections, and doubly excited configurations while maintaining spin purity. Extending this framework to unrestricted Kohn–Sham (UKS) orbitals introduces desirable variational flexibility but also leads to spin-asymmetric orbital instabilities that degrade numerical stability and distort excitation energies. In this study, we identify the origin of these instabilities in the residual mismatch between the α and β spatial orbitals of UKS references and introduce a selective Jacobi-rotation procedure that systematically maximizes α–β orbital overlap without altering the UKS reference energy or mixing occupied and virtual spaces. Numerical tests on thymine and s-trans-butadiene demonstrate that the Jacobi-rotated orbitals eliminate anomalous orbital-overlap patterns, suppress geometry-dependent fluctuations of UMRSF-TDDFT energies, and recover smooth and physically consistent potential energy surfaces. Benchmarking against Thiel’s TBE-2 set further confirms that UMRSF-TDDFT preserves the accuracy of the original MRSF-TDDFT while benefiting from improved orbital flexibility. The resulting approach restores numerical stability to the unrestricted formulation and broadens the applicability of MRSF-TDDFT to systems requiring enhanced spin polarization or exhibiting strong multiconfigurational character.